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Comparing Characteristics of Quadratic Functions Essential Questions: How do you compare two quadratic functions? Warm-Up 3 (2.27.2014) 1. Find the zeros, find the maximum or minimum, y-intercept, axis of symmetry, then sketch the graphs. A. x2 – x – 20 = 0 B. x2 + 8x + 15 = 0 CCM 2 Name: Round 1: Projectiles and Parabolas Look at the two trajectories above. 1. What is the same about the two equations? 2. What does the y-intercept represent? What part of the equation gives you the yintercept? 3. What do the x-intercepts represent? 4. The highest part of the bird’s flight is represented by what part of the parabola? 5. A. How far does Angry Bird fly in h(x)? B. How high does he go? C. How far away from the catapult is he when he is at his highest? D. When he is 15 feet away, how high is he flying? Characteristics (or Extrema ) of Quadratics: •X-intercepts •the zeros or solutions of the quadratic •Y-intercept •when x=0 •where the quadratic crosses the y-axis) •Minimum or Maximum •the Vertex • the x-value of the vertex is the average of the zeros •Axis of symmetry (NEW) •The line the parabola is reflected over •Will always be an “x = #” line •Always the line “x = the x-value of the vertex” b •Another way to fins this is x 2a •use this way if you cannot easily factor the quadratic Round 2 1. When Angry Bird is 9 feet away, how high is he flying? 2. The axis of symmetry is provided. A. What part of the parabola does this pass through? B. What does this part represent about Angry Bird’s flight? 3. How high does the bird fly? 4. Reflect points over the axis of symmetry to complete the parabola. Do you hit any pigs? 5. How far would Angry Bird fly if he did not hit any obstacles? 6. Without solving for the whole equation, A. What is “c” value in standard form? B. Is “a” positive or negative? Round 3 1. Angry bird is at (0,0). Angry bird and hungry pig are 18 feet away from each other. If angry bird and hungry pig are at the same height (y-value) when angry bird is catapulted, at what distance away is Angry Bird the highest? Hint: Think about symmetry. 2. Angry Bird wants to hit the pig on the right. The equation representing his flight is: y . 083 x 1 . 82 x 0 2 A. Using the picture, what is the y-intercept? B. Using the picture, what are the x-intercepts? C. Where is the axis of symmetry? You may use the picture to visualize, but show your algebraic work using: Round to the nearest integer. b x 2a D. How high does Angry Bird fly (rounded to the nearest integer)? E. Sketch the graph of Angry Bird’s flight. Comparing Quadratics of different forms. •An equation (You can covert this to a graph) •A graph •A table (You can find the quadratic regression line, then graph) Black Bird Black Bird’s flight path can be modeled by the quadratic equation y x 2 28 x 171 Maximum Height________ Axis of Symmetry_________ Distance Traveled: ____________ Red Bird Red Bird’s flight is represented by the graph: Maximum Height________ Axis of Symmetry_________ Distance Traveled: ____________ Blue Bird The table below contains data points of Blue Birds flight trajectory. X 2 3 4 5 6 7 8 9 10 y 0 9 16 Maximum Height________ 21 24 25 24 21 16 Axis of Symmetry_________ Distance Traveled: ____________ Complete Angry Birds Part 2 for Class Work Exit Ticket 1. 2. 3. 4. 5. 6. Can you multiply binomials? Can you factor when a = 1? Can you factor when a is NOT 1? Can you find the vertex? Can you find the y-intercept? Can you write a quadratic equation given any condition? HW: